Superoscillation in speckle patterns

Mark R. Dennis, Alasdair C. Hamilton, Johannes Courtial
2008 Optics Letters  
Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability density function of intensity and phase gradient for isotropic gaussian random wave superpositions. Strikingly, this fraction is 1/3 when all the waves in the two-dimensional superposition have the same wavenumber. The fraction is 1/5 for a disk spectrum.
more » ... a disk spectrum. Although these superoscillations are weak compared with optical fields with designed superoscillations, they are more stable on paraxial propagation.
doi:10.1364/ol.33.002976 pmid:19079511 fatcat:ge4adyuhwzgjtcqyplo3bby5s4